Solve for $x$ and $y$ using elimination. ${-x+3y = 4}$ ${x-5y = -12}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-x+3y = 4}\thinspace$ to find $x$ ${-x + 3}{(4)}{= 4}$ $-x+12 = 4$ $-x+12{-12} = 4{-12}$ $-x = -8$ $\dfrac{-x}{{-1}} = \dfrac{-8}{{-1}}$ ${x = 8}$ You can also plug ${y = 4}$ into $\thinspace {x-5y = -12}\thinspace$ and get the same answer for $x$ : ${x - 5}{(4)}{= -12}$ ${x = 8}$